Equilibrium payoffs in finite games

Ehud Lehrer (), Eilon Solan () and Yannick Viossat
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Ehud Lehrer: TAU - Tel Aviv University

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Abstract: We study the structure of the set of equilibrium payoffs in finite games, both for Nash equilibrium and correlated equilibrium. A nonempty subset of R^2 is shown to be the set of Nash equilibrium payoffs of a bimatrix game if and only if it is a finite union of rectangles. Furthermore, we show that for any nonempty finite union of rectangles U and any polytope P in R^2 containing U, there exists a bimatrix game with U as set of Nash equilibrium payoffs and P as set of correlated equilibrium payoffs. The n-player case and the robustness of this result to perturbation of the payoff matrices are also studied.

Keywords: equilibrium payoffs; correlated equilibrium (search for similar items in EconPapers)
Date: 2011
Note: View the original document on HAL open archive server: https://hal.science/hal-00361914
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Published in Journal of Mathematical Economics, 2011, 47, pp.48-53. ⟨10.1016/j.jmateco.2010.10.007⟩

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Journal Article: Equilibrium payoffs of finite games (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00361914

DOI: 10.1016/j.jmateco.2010.10.007

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